, Volume 26, Issue 2, pp 143–145 | Cite as

The flexure of infinite rectangular plates of varying thickness

  • H. D. Conway


It will be seen that the deflection and moment Mx are both zero on edges xa, ±3 a,... Hence the above solution is also valid for a plate of finite length simply supported on any two of these edges.

So far as the variable thickness version of MacGregor's single concentrated load case is concerned, the loading is written in the Fourier integral form
$$Q_{y = a} = \frac{P}{{\pi a}}\int\limits_0^\infty {\cos \gamma xd(\gamma a)}$$
and the deflections are given by the Fourier integral
$$\omega = \frac{1}{a}\int\limits_0^\infty {(A_1 e^{\lambda _1 y} + B_1 e^{\lambda _2 y} + C_1 e^{\lambda _3 y} + D_1 e^{\lambda _4 y} )\cos } {\text{ }}\gamma xd(\gamma a).$$

The evaluation of this integral must be performed numerically after the value of the thickness constant b has been selected to best fit the actual variation. This may be done by computing the integrand over a certain range for various values of γa and evaluating the integral in this range by Simpson's rule.

Beyond this range, the integrand may be written in simpler form and the integral evaluated in closed form. This involves considerable labor and, since the calculations must be repeated for each value of b selected, they will not be made here. Numerical calculations of Fourier integrals such as the above have been made by Girkmamn7 and the author8.


Neural Network Fourier Complex System Numerical Calculation Information Theory 
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Copyright information

© Springer-Verlag 1958

Authors and Affiliations

  • H. D. Conway
    • 1
  1. 1.Thurston Hall, Cornell UniversityIthacaUSA

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